Question: Simplify the following expression: $ n = \dfrac{x - 1}{-5x + 7} - 7 $
In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-5x + 7}{-5x + 7}$ $ \dfrac{-7}{1} \times \dfrac{-5x + 7}{-5x + 7} = \dfrac{35x - 49}{-5x + 7} $ Therefore $ n = \dfrac{x - 1}{-5x + 7} + \dfrac{35x - 49}{-5x + 7} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{x - 1 + 35x - 49}{-5x + 7} $ $n = \dfrac{36x - 50}{-5x + 7}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-36x + 50}{5x - 7}$